I was told by Tricare that the TRS was not active until the 1st of the month after you sign up. For example lets say you separate or go off AD on 31MAY, join the reserves or reaffiliate with your reserve unit/Guard on 1 JUN and sign up for TRS on 1JUN. Your coverage does not start until 1JUL. The Bridge(to my knowlege the military does not offer a Cobra plan) plan is good but can only be purchased on a quarterly basis and is not refundable(pro-rated). So you conceivably would have a gap in coverage or pay for 2 extra months of a bridge plan that you didnt use at a much higher rate(it's roughly 1300/quarter)
I chose to use my company's health care plan. I live in a military saturated area and Tricare care providers out in town are shotty at best. I'll pay the extra 50/month and co pays for a solid health care plan for my family, its well worth it, especially with young children.